The present invention relates to, inter alia, noise extraction from a signal. The signal may be used, for example, in the generation of images from projection measurements. Examples of images generated from projection measurements include two-dimensional and three-dimensional SAR (synthetic aperture radar) systems. SAR is a form of radar in which the large, highly-directional rotating antenna used by conventional radar is replaced with many low-directivity small stationary antennas scattered over some area near or around the target area. For example, as shown in FIG. 1 of U.S. Pat. No. 5,805,098 to McCorkle, hereby incorporated by reference, an aircraft mounted detector array is utilized to take ground radar measurements. Other examples of systems using projection measurements are fault inspection systems using acoustic imaging, submarine sonar for imaging underwater objects, seismic imaging system for tunnel detection, oil exploration, geological surveys, etc., and medical diagnostic tools such as sonograms, echocardiograms, x-ray CAT (computer-aided tomography) equipment and MRI (magnetic resonance imaging) equipment.
Wide-bandwidth signals are widely used in communications and radar systems. Over the past few decades, the research and development of ultra-wideband (UWB) systems have achieved significant progress. One of the key features of these UWB systems is the penetration capability. For example, the U.S. Army has been developing UWB radar systems for detection of difficult targets in various applications such as foliage penetration, ground penetration, and sensing through the walls of buildings or harriers (sensing-through-the-wall). Therefore, these systems must operate in the low-frequency spectrum that spans from under 100 MHz to several GHz in order to achieve the penetration capability. In addition to the low-frequency requirement for penetration, the systems must employ wide-bandwidth signals to achieve the desired resolution. Thus, the signal occupies a wide spectrum that also shared by radio, TV, cellular phone, and other systems. For example, radio waves in general usage have wavelengths ranging from hundreds of meters to about one millimeter and are used for transmission of data, via, modulation. Television, mobile phones, wireless networking, and amateur radio all use radio waves. The use of the radio spectrum is regulated by many governments through frequency allocation.
The frequency allocation and utilization problem becomes a big challenge and only gets worse over time since additional radar and communication systems that need the penetration feature must operate in this low-frequency region of the spectrum. The FCC and international treaties in general restrict the hands between 5 and 30 MHz, since they are particularly useful for long-distance communications.
There are at least two challenges for any UWB system (radar or communications). The first is that the system must operate in the presence of other systems. The received UWB signal through the channel is contaminated by signals from all systems that operate in the same spectrum. Because of this, the received signal would have a spectral content that includes many frequency subbands that are corrupted by energy from all other sources. Within these corrupted subbands, the energy of the received signal is much smaller than that from the interference sources. In the time domain, the signal is very noisy and might be embedded in the noise floor. Except for targets with very large amplitudes, most targets may not be detectable in the presence of interference noise. Conventional techniques usually detect the corrupted frequency bands (due to the interference sources) by searching for the spikes in the spectral domain. The fast Fourier transform (FFT) bins that correspond to the contaminated frequency bands are zeroed out. This technique results in severe sidelobes in the time or spatial domain of the output data and imagery due to the sharp transitions (frequency samples with no information) in the frequency domain. In addition, simply suppressing the information in the contaminated frequency bands will reduce the signal-to-noise ratio (SNR) of the received signal.
Interference signals from competing frequencies are essentially large amplitude noise that often masks the underlying radar signals. Various interference noise suppression techniques have been proposed to date. The simplest approach that has been widely employed in practice involves implementing adaptive notch filters (whose notches in the frequency domain correspond to interference noise components) to suppress the energy from interference noise signals. Depending on the nature of the interference noise sources, this notch-filter approach would result in (i) large sidelobes in the time domain of the received signal and (ii) reduced target amplitudes. It is generally desirable to extract the interference noise from signal in time domain for best performance. To avoid, the side effects of the notch-filter implementation. Miller et al., “RFI Suppression for Ultra Wideband Radar,” IEEE Transactions on Aerospace and Electronic Systems, vol. 33, no. 4, (October 1997) (herein incorporated by reference) proposes another interference noise suppression technique that estimates the noise components and subtracts (in the time domain) the estimated noise signal from the received radar signal. However, the technique requires complete knowledge of the interference sources. The technique is based on the assumption that the interference sources consist of a number of narrowband amplitude modulation (AM) and frequency modulation (FM) channels. This assumption is no longer valid with the current frequency spectrum, in which most of the communications and TV channels are broadcasting using various digital modulation schemes. Within each communications channel, the radio frequency (RF) signal looks like white noise in the time domain with its amplitude and phase quickly varying with respect to time. Thus, it is not possible to use the Miller technique to estimate these RF interference (RFI) components with digital modulation contents.
Another challenge for any UWB system (radar or communications) is that the system must avoid transmitting energy in certain frequency bands that are specified by the frequency management agencies. Thus, the received UWB signal would have a spectral content that is not contiguous (due to spectral notches that correspond to the prohibited frequency bands). The notches in the frequency domain translate to severe noise and artifacts in the resulting data and imagery. Depending on the size of the spectral notches, state-of-the-art systems might have to process each contiguous band separately to get results from multiple bands. Since the results from multiple bands are interpreted independently, this creates another challenge for the detection and discrimination stages.